simulation problem/Project Euler #307

I have written a short simulation program (two short functions) for this problem

k defects are randomly distributed amongst n integrated-circuit chips produced by a factory (any number of defects may be found on a chip and each defect is independent of the other defects).

Let p( k,n) represent the probability that there is a chip with at least 3 defects. For instance p(3,7) ≈ 0.0204081633.

I've written the simulation program as given in https://github.com/jfredett/euler/blob/master/c/problem-307/README-307.mkd

However,it gives 2 orders smaller probability for the toy example p(3,7),see the bottom of the email. WHY??I do not see any problem either with the approach nor with my application. Here are the two functions:

function [succ,E]=recur(k,n)

E=zeros(1,n);

succ=0;

while k>0

for i=1:n

if rand>0.5 E(i)=E(i)+1;k=k-1;end;

end;

if max(E)>2 succ=1;E,return,end;

end

return

--------------------------------------------

function res=recur2(k,n,m)

suc=0;

for i=1:m

suc=suc+recur(k,n);end;

res=suc/m

return

--------------------------------------------

recur2(3,7,1000000)

ans =

2.3900e-04